Rennela, Mathys and Staton, Sam - Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory

lmcs:4068 - Logical Methods in Computer Science, March 10, 2020, Volume 16, Issue 1
Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory

Authors: Rennela, Mathys and Staton, Sam

We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. We show that this structure is also related to linear/non-linear models. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types.


Volume: Volume 16, Issue 1
Published on: March 10, 2020
Submitted on: November 15, 2017
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,Mathematics - Category Theory,Mathematics - Operator Algebras,Quantum Physics,F.3.2


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